Finite Group Databasebeta

← #46783194

Subgroups — #46783194

Order 33664.

358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30682450C211yesmaximal, characteristic
2C2×#22554427C211yesmaximal, characteristic, complemented
3C2×#22554398C211yesmaximal, characteristic, complemented
4C2×#22554396C211yesmaximal, characteristic, complemented
5#30681901C211yesmaximal, characteristic, complemented
6#30681697C211yesmaximal, characteristic, complemented
7#339×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9C22×C4×D263C2211yescharacteristic
10C2×#16862360C2211yescharacteristic
11#22554454—21no—
12#22554450C412yescomplemented
13#22554445C412yescomplemented
14#22554440—21no—
15C4×D1052—22no—
16#22554427—22no—
17#22554427—22no—
18C2×Dic263⋊C4—21no—
19C2×(C2×D263)⋊C4—21no—
20C2×C4×Dic263C2211yescharacteristic
21#22554398—22no—
22#22554396—22no—
23(C2×D263)⋊C8—22no—
24C2×M16×C263C2211yescharacteristic
25#117×C263C2211yescharacteristic
26C2×C42×C263C2211yescharacteristic
27C23×D263D411yescharacteristic
28#16862376—21no—
29#16862376—21no—
30#16862376—21no—
31#16862376—21no—
32C2×Dic526C2×C411yescharacteristic
33C2×D1052—22no—
34C2×D1052C2×C411yescharacteristic
35C2×C22⋊D263—21no—
36C22×Dic263—21no—
37C22×Dic263D411yescharacteristic
38C2×C4×D263—21no—
39C2×C4×D263—21no—
40C2×C4×D263—21no—
41C2×C4×D263—21no—
42C2×C4×D263—21no—
43C2×C4×D263C2×C412yes—
44C2×C4×D263D412yes—
45#16862360—21no—
46#16862360—21no—
47C2×C263⋊C8—21no—
48C4⋊Dic263—22no—
49Dic263⋊C4—24no—
50(C2×D263)⋊C4—24no—
51(C2×D263)⋊C4—22no—
52(C2×D263)⋊C4—22no—
53C4×Dic263—21no—
54C4×Dic263D412yescomplemented
55C22×C4×C263—21no—
56C22×C4×C263C2311yescharacteristic
57M16×C263—21no—
58M16×C263—21no—
59C2×C8×C263—21no—
60C4⋊C4×C263C2×C412yes—
61C22⋊C4×C263—21no—
62C42×C263—21no—
63C42×C263—21no—
64C42×C263D412yescomplemented
65C22×D263—21no—
66C22×D263—21no—
67C22×D263—21no—
68C22×D263—42no—
69C22×D263C22⋊C412yes—
70Dic526—21no—
71Dic526—21no—
72D1052—21no—
73D1052—21no—
74D1052—44no—
75C22⋊D263—41no—
76C22⋊D263—41no—
77C2×Dic263—21no—
78C2×Dic263—21no—
79C2×Dic263—21no—
80C2×Dic263—22no—
81C2×Dic263—42no—
82C2×Dic263C22⋊C412yes—
83C4×D263—22no—
84C4×D263—22no—
85C4×D263—22no—
86C4×D263—22no—
87C4×D263—41no—
88C4×D263—41no—
89C263⋊C8—41no—
90C23×C263C2×D411yescharacteristic
91C2×C4×C263—22no—
92C2×C4×C263—22no—
93C2×C4×C263—42no—
94C2×C4×C263C22×C411yescharacteristic
95C2×C4×C263C2×D411yescharacteristic
96C2×C4×C263C2×D411yescharacteristic
97C2×C4×C263C2×D411yescharacteristic
98C2×C4×C263#4111yescharacteristic
99C2×C4×C263#4111yescharacteristic
100C8×C263—41no—
101C22×C263—22no—
102C22×C263C2×C22⋊C411yescharacteristic
103C22×C263#12011yescharacteristic
104C22×C263#12311yescharacteristic
105C2×D263—22no—
106C2×D263—22no—
107C2×D263—22no—
108C2×D263—42no—
109C2×D263—42no—
110C2×D263—41no—
111C2×D263—42no—
112C4×C263—42no—
113C4×C263—42no—
114C4×C263C4×D411yescharacteristic
115C4×C263C4×D411yescharacteristic
116C4×C263#12111yescharacteristic
117C4×C263#12111yescharacteristic
118Dic263—22no—
119Dic263—42no—
120Dic263—41no—
121C2×C263—21no—
122C2×C263—21no—
123C2×C263#38611yescharacteristic
124C2×C263#42112yes—
125D263—42no—
126D263—81no—
127C263#189711yescharacteristic, complemented, Sylow
128#1897—2631nomaximal, Sylow
129#525—2631no—
130C2×#117—2631no—
131C2×#104—2631no—
132C2×#104—2631no—
133#407—2631no—
134#339—2631no—
135#339D26311yescharacteristic, complemented
136C2×#41—2631no—
137C23×C4—2631no—
138C2×M16—2631no—
139C2×M16C2×D26311yescharacteristic
140#123—5261no—
141C22⋊Q8—2632no—
142#121—2632no—
143#120—5261no—
144C4×D4—5262no—
145#117—5262no—
146#117—5262no—
147#117C2×D26311yescharacteristic
148C2×C4⋊C4—5261no—
149C2×C22⋊C4—5261no—
150C2×C42—2631no—
151C2×C42C2×D26311yescharacteristic
152#104—5262no—
153#104—5262no—
154C22⋊C8—5262no—
155C24—2631no—
156#41—5261no—
157#41—5261no—
158#41—5261no—
159#41—5261no—
160C2×Q8—2631no—
161C2×D4—2631no—
162C2×D4—5262no—
163C2×D4—5261no—
164C22×C4—21no—
165C22×C4—2631no—
166C22×C4—2632no—
167C22×C4—2632no—
168C22×C4—5261no—
169C22×C4—5261no—
170C22×C4—5261no—
171C22×C4—5261no—
172C22×C4—5261no—
173C22×C4—5261no—
174C22×C4C22×D26311yescharacteristic
175M16—21no—
176M16—21no—
177M16—5261no—
178M16—5261no—
179C2×C8—21no—
180C2×C8—5261no—
181C4⋊C4—5262no—
182C4⋊C4—5264no—
183C4⋊C4C4×D26312yes—
184C22⋊C4—21no—
185C22⋊C4—5262no—
186C22⋊C4—5262no—
187C22⋊C4—5264no—
188C42—21no—
189C42—21no—
190C42—2632no—
191C42—5261no—
192C42D105212yescomplemented
193C23—2632no—
194C23—5261no—
195C23—5261no—
196C23—5261no—
197C23—10522no—
198C23D4×D26311yescharacteristic
199Q8—5261no—
200Q8—5261no—
201D4—5261no—
202D4—5261no—
203D4—10524no—
204D4—10521no—
205D4—10521no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—2632no—
210C2×C4—5261no—
211C2×C4—5261no—
212C2×C4—5262no—
213C2×C4—5262no—
214C2×C4—5262no—
215C2×C4—5262no—
216C2×C4—5261no—
217C2×C4—5262no—
218C2×C4—10522no—
219C2×C4—10521no—
220C2×C4—10521no—
221C2×C4C2×C4×D26311yescharacteristic
222C2×C4D4×D26311yescharacteristic
223C2×C4D4×D26311yescharacteristic
224C2×C4C2×D105211yescharacteristic
225C2×C4#1686237611yescharacteristic
226C2×C4#1686237711yescharacteristic
227C8—41no—
228C8—10521no—
229C22—22no—
230C22—5262no—
231C22—5262no—
232C22—5262no—
233C22—10522no—
234C22—10522no—
235C22—10522no—
236C22—10521no—
237C22C22⋊C4×D26311yescharacteristic
238C22#2255444011yescharacteristic
239C22#2255445511yescharacteristic
240C4—42no—
241C4—42no—
242C4—5262no—
243C4—10522no—
244C4—10521no—
245C4#2255443211yescharacteristic
246C4C4×D105211yescharacteristic
247C4#2255444311yescharacteristic
248C4#2255444511yescharacteristic
249C2—21no—
250C2—21no—
251C2—10522no—
252C2—21041no—
253C2#3068181611yescharacteristic
254C2#3068195312yes—
subgroupG/H
centerC2×C4D4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#339×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682450C2
cosocleC22×C4×C263C23
hypercenter#339D263
hypocenterC263#1897
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#22554427C2semidirect
3. C2×#22554398C2semidirect
4. C2×#22554396C2semidirect
5. #30681901C2semidirect
6. #30681697C2semidirect
7. #339×C263C2semidirect
12. #22554450C4semidirect
13. #22554445C4semidirect
54. C4×Dic263D4semidirect
64. C42×C263D4semidirect
127. C263#1897semidirect
135. #339D263semidirect
192. C42D1052semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#306824502
C2×#225544272
C2×#225543982
C2×#225543962
#306819012
#306816972
#339×C2632
#1897263